n = number of compounding periods per unit t; at the END of each period

Compound Interest Formulas and Calculations:

Calculate Accrued Amount (Principal + Interest)

A = P(1 + r/n)nt

Calculate Principal Amount, solve for P

P = A / (1 + r/n)nt

Calculate rate of interest in decimal, solve for r

r = n[(A/P)1/nt - 1]

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / n[ln(1 + r/n)] = [ ln(A) - ln(P) ] / n[ln(1 + r/n)]

Formulas where n = 1 (compounded once per period or unit t)

Calculate Accrued Amount (Principal + Interest)

A = P(1 + r)t

Calculate Principal Amount, solve for P

P = A / (1 + r)t

Calculate rate of interest in decimal, solve for r

r = (A/P)1/t - 1

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = t = ln(A/P) / ln(1 + r) = [ ln(A) - ln(P) ] / ln(1 + r)

Continuous Compounding Formulas (n → ∞)

Calculate Accrued Amount (Principal + Interest)

A = Pert

Calculate Principal Amount, solve for P

P = A / ert

Calculate rate of interest in decimal, solve for r

r = ln(A/P) / t

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / r

Example Calculation

I have an investment account that increased from $30,000 to $33,000 over 30 months. If my local bank offers savings account with daily compounding (365), what annual interest rate do I need to get from them to match the return I got from my investment account?

In the calculator select "Calculate Rate (R)". The equation the calculator will use is: r = n[(A/P)1/nt - 1] and R = r*100.